In case this might be helpful for anyone else...
I did some checking and from what I found, ashes are placed in a plastic bag, and then that is placed in a temporary plastic box, or cardboard box. I called a local company and also checked online for the size of the plastic container - typically 8.5x6.5x4.5 (exterior dimensions in inches) although I guess there are varying sizes.
I think I'll build so the temporary box can just slide into the wooden urn. That will also help me finalize the shape as I was debating between a cube vs rectangular. To slide in this temporary box, it will be the latter.